An integral transform technique for gyrokinetics

The linearized Vlasov-Poisson system can be exactly solved using the G-transform, an integral transform that removes the electric field term, leaving a simple advection equation. We apply this integral transform to the gyrokinetic equations. The commutator of the collision operator with the G-transform (the ``shielding term'') is negligible and the G-transform leaves the nonlinear perpendicularity unchanged. Since it is often useful to represent parallel velocity space in terms of Hermite polynomials, we state an explicit calculation of their G-transform. We implement the G-transform in a gyrokinetic code and show how it can be used to simplify the dynamics.